Jagged and ugly Shadows in Eevee
This is caused by the inaccurate behavior of Shadow Mapping used in real time rendering enginnes like EEVEE and almost all game rendering engines. People call them Shadow Acne. 

What you see is actually pixelated shadow mapping to some boundary area, causing those alias shadow show on the mesh.

There are many solutions to overcome this problem, but since performance is the main issue in real-time rendering, the best solution changes depend on the situation of your application.

You can check out this explanation about shadow mapping: Shadow Mapping - LearnOpenGL



Blender 2.81 Update Information

According to the latest Blender,


  Soft shadows were changed and now enabled with the Use Soft Shadow option in the render properties Shadow panel. This will progressive smooth shadows, in combination with a more conventional shadow filtering method (PCF). Exponential and Variance Shadow Mapping methods were removed. (d8aaf25c23fa)


The way EEVEE render shadow has been changed to a more common method. And the problem of Shadow Acne should be reduce or even solved. Check for the latest Blender to see whether the shadow has been fixed.